WIAS Preprint No. 329, (1997)

Stability Analysis of Quadrature Methods for Two-Dimensional Singular Integral Equations



Authors

  • Abdel-Fattah, Ibrahim Saad

2010 Mathematics Subject Classification

  • 45L10 45Exx 65N38 65R20

Keywords

  • singular integral equation, two-dimensional manifold, quadrature method

Abstract

In this paper we apply a quadrature method based on the tensor product trapezoidal rule to the solution of a singular integral equation over the two-dimensional torus. We prove that this method is stable if and only if a certain numerical symbol does not vanish. For a special kernel function, we present a plot of numerically computed symbol values and, for symmetric kernels (Mikhlin-Giraud kernels), we show that the symbol is different from zero if the singular integral operator is invertible. Finally, we prove the convergence of our method and present numerical tests.

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